CUPERTINO — Seeking to give some older product designs new life, Apple on Monday announced an updated iPhone and an updated iPad.

The new phone, dubbed the iPhone SE, has the same basic shape as the iPhone 5, which the company first introduced in 2012. The new tablet, which gets an “iPad Pro” moniker, comes with a 9.7-inch screen, the same size as the first iPad model that Apple introduced in 2015.

Although both devices included updated innards, they allow Apple to offer new products in shapes and styles that are familiar to consumers.

“We’re really excited about the iPhone SE,” company CEO Tim Cook said at a press event at the company’s headquarters here. “Many, many customers have asked us for this, and I think they’re going to love it.”

Although the event was primarily designed to showcase the new devices, Cook took some time at the beginning of it to address, at least in passing, the company’s dispute with the FBI, which has been dominating most discussion of Apple of late. There are now 1 billion Apple devices in use around the world, and Apple’s customers store some of their most personal data on them, Cook noted. The company feels a “significant responsibility” to protect their data and their privacy, he said.

“We didn’t expect be in this position, at odds with our own government,” Cook said. But, he added, “We owe it to our customers and our country. This is an issue that affects all of us, and we will not shrink from this responsibility.”

At the relatively small event, held in the same “Town Hall” theater where Apple introduced the iPod and the iPhone App Store, Cook and his colleagues announced new versions of iOS, the software underlying the iPhone and iPad, and tvOS, the software underlying the new Apple TV. They also showed off some new bands for Apple Watch and introduced CareKit, a new platform that can be used by health providers to create applications that patients can use to monitor their own care.

But the primary focus was on the two new devices. The iPhone SE, which will be released March 31, is basically an iPhone 6S in an iPhone 5’s body. It has the same chip and camera and the iPhone 6S and will be able to take “live photos,” the pictures that capture a bit of video before and after the moment when the picture is taken.

Perhaps the most significant thing about the iPhone SE is its price. Apple will charge $400, without a carrier contract, for the base model of the new phone. That marks the lowest price ever for a brand new iPhone and could help the company attract more budget-minded consumers.

With the new iPad Pro, Apple is taking a similar, if pricier, tack. The device represents a complete overhaul of the iPad Air 2. It has the same high-powered chip as the iPad Pro, the same four-speaker set-up for audio, and the same camera that’s in the iPhone 6s.

The new device starts at $600 for a 32-gigabyte model. That’s about $100 more than Apple typically charges for a brand new 9.7-inch iPad. But it’s $200 less than than 12-inch iPad Pro.